Use the substitution method to solve the system of equations. Choose the correct ordered pair.x + y = 5 y = 7

Answers

Answer 1

Answer: First we put 7 in the place of y, after that subtract 7 from both sides, the answer is -2.
x + y= 5 y = 7
x+ 7=5
x= 5-7
x = -2

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If T(n) = 6n + 2 what is the 3rd term

Answers

To find the 3rd term, just replace the 'n' with 3.

Therefore:

t(3) = 6(3) + 2
t(3) = 18 + 2
t(3) = 20.

The 3rd term is 20.

T(n)=6n+2 T3=6(3)+2 T3=20

A bicycle shop repaired 40 bicycles in 8 days. What was the rate of work?

A.

B.

C.

D.

Answers

40÷8= 5
they repaired on average 5 bikes per day

The bike shop repairs 40/8=5 bicycles per day, on average.

Joe solved this linear system correctly.6x+3y=6

y=−2x+2

These are the last two steps of his work.

6x−6x+6=6

6=6

Which statement about this linear system must be true?

a) x must equal 6

b) y must equal 6

c) there is no solution to this system

d) there are infinitely many solutions to this system

Answers

There are infinitely many solutions because the first two equations are actually the same just arranged differently so there's not enough information to know what x or y are in other words they could be anything.

The table below shows the number of hours some business people in two states spend in meetings each week:State A
21 23 24 22 24 25 23 23 22
State B
24 22 20 23 23 50 20 46 21

Part A: Create a five-number summary and calculate the interquartile range for the two sets of data.

Part B: Are the box plots symmetric? Justify your answer.

Answers

Arrange data set in ascending order:
State A: 21, 22, 22, 23, 23, 23, 24, 24, 25
State B: 20, 20, 21, 22, 23, 23, 24, 46, 50

State A State B
minimum 21 20
1st Quartile 22 20.5
median 23 23
3rd Quartile 24 46
maximum 25 50
IQR 2 25.5

In Chemistry class, Andrew has earned scores of 64, 69, and 73 on three tests. He must maintain an average of 70 to pass the course. What score must Andrew earn on the final exam to pass the course?

Answers

64 + 69 + 73 = 206 ÷ 3 = 68 ish
if he get at least 74 :
64 + 69 + 73 + 74 = 280 ÷ 4 = 70
he will pass course with straight 70

The area of a rectangular wall of a barn is 108 square feet. Its length is 12 feet longer than the width. Find the length and width of the wall of the barn.

Answers

Area = Width x Length
Area = 108
Square root of 108 = 10.4

108/ 9 = 12 ...12 is not 12 larger than 9
108/ 6 = 18 ...18 is 12 larger than 6

108 = 6 x 18

Width = 6
Length = 18

Final answer:

To find the length and width of the wall of the barn, set up an equation using the given information. Solve the equation by factoring, and find the values of x and x + 12, which will be the width and length of the wall, respectively. The width of the wall is 6 feet, and the length is 18 feet.

Explanation:

To find the length and width of the wall of the barn, we can use algebra. Let's say the width of the wall is x. According to the problem, the length is 12 feet longer than the width, so the length is x + 12.

The area of a rectangle is found by multiplying the length by the width, so we can set up the equation

x(x + 12) = 108.

Solving this equation will give us the values of x and x + 12, which will be the width and length of the wall, respectively.

The equation is x(x + 12) = 108.

Expanding the equation gives x^2 + 12x = 108.

Rearranging the equation to bring everything to one side gives

x^2 + 12x - 108 = 0.

Factoring the quadratic equation gives (x + 18)(x - 6) = 0.

Setting each factor equal to zero gives x = -18 or x = 6.

Since we can't have a negative width, the width of the wall is 6 feet.

Therefore, the length of the wall is x + 12 = 6 + 12 = 18 feet.